One of the spurious claims being circulated by the Birther fringe is that one of President Obama's first acts in office was to issue Executive Order 13489 (PDF), which they claim was intended to seal away his birth certificate, school records and other evidence that he is not a United States citizen or otherwise unqualified to be President.
However, this executive order is virtually the same as Executive Order 123283 (PDF), which President George W. Bush issued early in his presidency and which it replaced. That executive order is in turn virtually identical to its predecessor Executive Order 12667 which was issued by President Reagan. All of these orders deal specifically with the National Archive and its role in preserving presidential papers and records. The orders refer only to records generated by the office of the President during his administration which have been kept by the National Archive since that institution was created in 1934.
Starting with Reagan it has been the practice of successive presidents to keep their operating records secret until a later date when they are made public as part of the comprehensive record of their presidency. This concern over the secrecy of White House records clearly originated in the aftermath of the Nixon presidency, which explains the discussion of executive privilege in the orders in question. It's equally clear that none of these prior presidents had any interest in concealing President Obama's birth records.
However, what none of these Executive Orders have any authority over are documents which were not generated by the President's office while he was serving. They do not apply to state records like birth certificates or private records like school transcripts. The President does not have the authority to seal those records by executive order even if he wanted to, and nothing in these Executive Orders even attempts to do so.
This is a classic example of people looking at a document with a conclusion already in mind, and mistakenly assuming that the document they are looking at supports their preconceived conclusion solely because of some superficial characteristic which may not actually be relevant. In this case the logical fallacy is the assumption that if President Obama is keeping records secret those records must relate to his birth certificate or school records because you already believe those things to be falsifications which he would want to cover up.
This is an example of the Existential fallacy or Vacuous Truth fallacy which is often demonstrated in the classic False Antecedent Syllogism. In this case:
To those already inclined to belief this may sound good, but in fact there is no proven foundation for the first assertion and no actual causal link between the second premise and the conclusion. It's a compound logical error originating with that unproven assumption which the evidence introduced doesn't actually support despite all claims..
This problem of misreading documents which have some superficial elements that can be misconstrued by those inclined to look for nefarious meanings is remarkably common. It becomes even worse when the documents deal with legal terms or concepts which the readers are unfamiliar with, or when they use foreign phrases, usually in Latin, which can be easily mistranslated to produce nonsensical or self-serving results.
Entire pyramids of conspiracy theory are built on this kind of illogic, and their delusional adherents will cling to them relentlessly so that their entire delusional world view isn't brought crashing down by pointing out their foundational error.